Lost in Math: Beauty != truth

A review of Sabine Hossenfelders book, Lost in Math: How Beauty Leads Physics Astray begs for a Hamlet introduction. Phrases like “something is rotten at the heart of theoretical physics” fly about like vampire clichés, ready to suck the joy out of any passing writer.

Nevertheless, Hossenfelder is sounding that alarm by suggesting that perhaps theoretical physicists need to spend a little more time on introspection and examining some of their working assumptions. Theoretical physics has been starved of new data for more than an entire generation. How can a theoretician choose a good model in the absence of data? And how do you choose which experimental options to pursue based on competing theoretical models?

Hossenfelder, whos a theoretical physicist herself, argues that physicists solution to this problem is an aesthetic one, not a scientific one—and the generation-long failure means aesthetics arent the right choice here.

Standards

In Lost in Math, Hossenfelder delves briefly into the history of particle physics in order to explain the success of the Standard Model of particles and forces. She touches on why weve not had any unexplainable data from experimental particle physics for the last 50 years. She then takes us on a tour of the data that make us think we should be looking for physics that is not explained by the Standard Model—dark matter, dark energy, and cosmic inflation.

All of this goes into explaining how theoretical physics seems to want to change the rules of what defines science. Hossenfelder has documented theoretical physicists explaining that, although a theory cannot make measurable predictions by its very construction, it should still be considered a scientific theory.

But what makes a “good” theory in the absence of data? You and I might think that this would be predictions for new data and, yes, that plays a role. But Hossenfelder takes us into a realm where theories are decades from being tested. Unfortunately, we need to evaluate their quality now so we can determine how much effort we put into preparing for those tests. What is the criteria for that?

Finding beauty in unity

The answer is… ugly. Theoreticians make the following sorts of arguments: the Standard Model is described by math that physicists find beautiful; therefore, we insist that new physics be described by mathematical beauty. Thats paired with another argument, termed naturalness. What is naturalness? It turns out that everything should be about equal to one. If a theory produces a very large number, that is OK, as long as it also produces another very large number so that the difference or ratio of the two is, you guessed it, roughly unity. One is the most natural and only acceptable answer. Any other answer is unnatural because it is unlikely to occur by chance.

Hossenfelder travels the world and talks to pretty much every big name in the field. She talks to string theorists, she covers supersymmetric theories, and she goes to the beach to talk to Lisi about his ideas on group theory. In all of this, Hossenfelder is hoping to find some unspoken justification for choosing beauty and naturalness as good standards.

Lost in Math does not just rely on interviews though. Hossenfelder shows us exactly how beauty and naturalness have lead us astray. Supersymmetry was attractive because it was natural and beautiful. Unfortunately, results from the Large Hadron Collider have eliminated natural versions of supersymmetry. If it turns out that the world is supersymmetric, the theory will not be natural; it will be fine tuned, with some unusual numbers that are just baked in.

Yet, proponents of supersymmetry are still firmly attached to their ideas and still pushing them. Why? Because, even if supersymmetry isnt natural, its still beautiful.

Realitys ugliness

To counter this, Hossenfelder looks back at the history of physics. Physics has a graveyard that is full of beautiful ideas. Beautiful and wrong. And, as Hosenfelder points out, very few new theories are considered beautiful on arrival. Newtons contemporaries were appalled at his theory of gravity. They acknowledged that it worked, but where were the gears? How could the Moon be drawn to the Earth if there was nothing linking them? In short, it was an ugly hack that worked. Now, we think its beautiful.

Quantum mechanics was also considered ad hoc and ugly. And even within quantum mechanics, scientists found each others ideas ugly (even when they explained the same phenomena). Like Newtons theory of gravity, success has bred familiarity, and familiarity leads to love. Hossenfelders point is that beauty has led us astray as often (or more often) than it has guided us to an improved theory.

Many of the theoreticians that Hossenfelder interviews seem to fall into two classes: some argue that this time beauty and naturalness are right, or they acknowledge their biases but are determined to continue to operate within those biases. In that respect, the book presents a very disturbing picture of particle physics.

Lost in Math is a quick and relatively light read. Most of it is Hossenfelders personal journey to find the justification for beauty and naturalness. The journey is mostly entertaining and engaging. When she breaks off to dive into various theories of particle physics, the going doesnt get too tough. And, importantly, I think that you dont need to have a physics background—you will still get enough out of the theory parts to follow the arguments. You will come out the end of it knowing more about the culture of theoretical physics.

Unfortunately, Hossenfelder gets her point across rather early in the book. And then makes the point again in a multitude of different ways. It gets a bit predictable.

I can imagine that Hossenfelders book is going to lead to a reasonable amount of angry Internet shouting. You see, every large-scale experiment that we build today, like XENON100—a detector searching for dark matter—is not just a miracle of applied physics and engineering. The choices for the detector type were determined by picking a set of theoretical models for dark matter. But these models are restricted to beautiful and natural models. Theoreticians seem to have taken the hymn “All things bright and beautiful” as literal, but they would do well to remember the alternative version “All things dull and ugly” is equally valid.